Comparing different mass estimators for a large subsample of the {\it Planck}-ESZ clusters

Total mass is arguably the most fundamental property for cosmological studies with galaxy clusters. We investigate the present differences in the mass estimates obtained through independent X-ray, weak-lensing, and dynamical studies. We quantify the differences as the mean ratio 1-$b$=M$_{\rm HE}$/M$_{\rm WL,dyn}$, where HE refers to hydrostatic masses obtained from X-ray observations, WL refers to the results of weak-lensing measurements, and dyn refers to the mass estimates either from velocity dispersion or from the caustic technique. Recent X-ray masses reported by independent groups show average differences smaller than $\sim$10$\%$, posing a strong limit on the systematics that can be ascribed to the differences in the X-ray analysis when studying the hydrostatic bias. The mean ratio between our X-ray masses and the weak-lensing masses in the LC$^2$-single catalog is 1-$b$=0.74$\pm$0.06. However, the mean mass ratios inferred from the WL masses of different projects vary by a large amount, with APEX-SZ showing a bias consistent with zero (1-$b$=1.02$\pm$0.12), LoCuSS and CCCP/MENeaCS showing a significant difference (1-$b$=0.76$\pm$0.09 and 1-$b$=0.77$\pm$0.10, respectively), and WtG pointing to the largest deviation (1-$b$=0.61$\pm$0.12). At odds with the WL results, the dynamical mass measurements show better agreement with the X-ray hydrostatic masses, although there are significant differences when relaxed or disturbed clusters are used. The different ratios obtained using different mass estimators suggest that there are still systematics that are not accounted for in all the techniques used to recover cluster masses. This prevents the determination of firm constraints on the level of hydrostatic mass bias in galaxy clusters.